WOLFRAM

Wolfram Language & System Documentation Center

FromFiniteFieldIndex[ind,ff]

gives the element of the finite field ff with index ind.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
See Also
Related Guides
History
Cite this Page

FromFiniteFieldIndex

FromFiniteFieldIndex[ind,ff]

gives the element of the finite field ff with index ind.

Details

Examples

open all close all

Basic Examples  (1)

Create a matrix of finite field elements with given indices:

Wolfram Language code: FromFiniteFieldIndex[{{11, 12}, {21, 22}}, FiniteField[5, 2]]//MatrixForm

Scope  (3)

Create a finite field element with a given index:

Wolfram Language code: FromFiniteFieldIndex[1234, FiniteField[11, 3]]

Use a finite field in the exponential representation:

Wolfram Language code: FromFiniteFieldIndex[123, FiniteField[3, 5, "Exponential"]]

Create a vector and a matrix of finite field elements with given indices:

Wolfram Language code: FromFiniteFieldIndex[{111, 222, 333}, FiniteField[7, 3]]
Wolfram Language code: FromFiniteFieldIndex[{{123, 234, 345}, {456, 567, 678}}, FiniteField[97, 5]]//MatrixForm

Applications  (1)

Create a vector and a matrix of randomly generated finite field elements:

Wolfram Language code: FromFiniteFieldIndex[RandomInteger[{0, 80}, 3], FiniteField[3, 4]]
Wolfram Language code: FromFiniteFieldIndex[RandomInteger[{0, 80}, {3, 3}], FiniteField[3, 4]]//MatrixForm

Properties & Relations  (3)

For a single index, FromFiniteFieldIndex[ind,ff] is equivalent to ff[ind]:

Wolfram Language code: ff = FiniteField[11, 3]; FromFiniteFieldIndex[1234, ff] === ff[1234]

For a list of integers, ff[list] gives a single element with polynomial coefficients specified by list:

Wolfram Language code: ff[{123, 234, 345}]
Wolfram Language code: 123 + 234ff[{0, 1}] + 345 ff[{0, 1}] ^ 2

FromFiniteFieldIndex[list,ff] gives a list of elements with indices specified by list:

Wolfram Language code: FromFiniteFieldIndex[{123, 234, 345}, ff]

Use FiniteFieldIndex to get indices of field elements:

Wolfram Language code: FromFiniteFieldIndex[{123, 234, 345}, FiniteField[19, 2]]
Wolfram Language code: FiniteFieldIndex[%]

ToFiniteField converts integers to elements of the prime subfield:

Wolfram Language code: ToFiniteField[{123, 456, 789}, FiniteField[5, 7]]

FromFiniteFieldIndex gives finite field elements with specified indices:

Wolfram Language code: FromFiniteFieldIndex[{123, 456, 789}, FiniteField[5, 7]]
Wolfram Research (2024), FromFiniteFieldIndex, Wolfram Language function, https://reference.wolfram.com/language/ref/FromFiniteFieldIndex.html.

Text

Wolfram Research (2024), FromFiniteFieldIndex, Wolfram Language function, https://reference.wolfram.com/language/ref/FromFiniteFieldIndex.html.

CMS

Wolfram Language. 2024. "FromFiniteFieldIndex." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FromFiniteFieldIndex.html.

APA

Wolfram Language. (2024). FromFiniteFieldIndex. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FromFiniteFieldIndex.html

BibTeX

@misc{reference.wolfram_2026_fromfinitefieldindex, author="Wolfram Research", title="{FromFiniteFieldIndex}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/FromFiniteFieldIndex.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_fromfinitefieldindex, organization={Wolfram Research}, title={FromFiniteFieldIndex}, year={2024}, url={https://reference.wolfram.com/language/ref/FromFiniteFieldIndex.html}, note=[Accessed: 13-June-2026]}